Editor's note: Julian E. Zelizer is a professor of history and public affairs at Princeton University's Woodrow Wilson School. His new book, "Arsenal of Democracy: The Politics of National Security -- From World War II to the War on Terrorism," will be published this fall by Basic Books. Zelizer writes widely on current events.

PRINCETON, New Jersey (CNN) -- President Obama could be opening up an important debate with the Republican Party on Monday by meeting with his Cabinet and instructing them to outline specific plans for cutting their budgets.

"There will be no sacred cows, and no pet projects. All across America, families are making hard choices, and it's time their government did the same," Obama told Americans in his weekly radio address on Saturday.

This decision will anger progressive supporters of the administration, many of whom have been perpetually worried about a potential "grand bargain" that President Obama might want to obtain by pushing for cuts in domestic spending -- including Social Security and Medicare -- in exchange for the expansions of government he wants on the issues of environmental regulation and health care.

But the real target audience of this announcement about budget reductions is Republican legislators, not Democrats, and it is unclear how they will respond. One of the most striking features of President Obama's first 100 days is that, thus far, the discipline of congressional Republicans has been steadfast.

Even as conservatives have opened up a debate about the need to revitalize their movement by finding new voices and new ideas, Republicans in Congress have generally voted as if 2008 never happened. Few Republican legislators dissent from the party line, and they continue to vote against almost all of the administration's agenda. Bipartisanship on the economic stimulus bill consisted of the support of three Republicans in the Senate. Television host Bill O'Reilly said that the "president has polarized Americans."

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Now the president is again offering Republicans room to start negotiations and show that they are serious about bipartisanship, opening a possibility for action by the politicians who don't agree with the "Dr. No" strategy of Rep. Eric Cantor of Virginia.

By focusing attention on spending cuts in the middle of the budget debate that began in February, the GOP has an opportunity to start making more specific demands about what they seek to cut in exchange for their support for items on Obama's agenda.

While politics are now more polarized than ever, it is useful to remember that in the past, bipartisan deals have produced landmark pieces of legislation. In the 80th Congress -- which President Truman ironically made famous in his 1948 campaign against the "do-nothing" Congress -- the president and Michigan Republican Arthur Vandenberg worked together on passage of the Marshall Plan, the Truman Doctrine, and the National Security Act, which were all central to the fight against communism.

In 1964, Republican Everett Dirksen of Illinois agreed to vote to end the filibuster against President Johnson's civil rights legislation in exchange for provisions that the senator sought to protect business from the legislation.

In 1986, Democrats agreed to a tax reform bill from Ronald Reagan's administration that lowered overall rates in exchange for closing loopholes that benefited wealthy citizens. In 1990, President George H.W. Bush accepted tax increases pushed by the Democratic Congress for budget cuts as part of a deficit reduction plan.

To be sure, bipartisanship is not always good. The conservative coalition of southern Democrats and Republicans in Congress that lasted from 1938 through the 1970s did much damage in areas such as race relations by blocking progress on civil rights.

But there are moments when we need bipartisan deals to be struck so that we can obtain legislation that has the most durable base of political support and long-lasting effects. This is one such moment, as we are living through an extremely volatile economic period and are struggling with structural challenges like skyrocketing health care costs.

President Obama has continued to express interest in reaching agreements with the Republican Party.

In his first month as president, he agreed to change the economic stimulus bill by making substantial spending cuts which his supporters thought would undermine the impact of the program. Obama did not "nationalize" the banks and instead settled on a financial bailout program that put most of the risk on average taxpayers.

Republicans have not been willing to play ball, even as many of them privately fear the costs that will result to the political standing of the party. Nor should Republicans underestimate the political skill of President Obama -- as Hillary Clinton learned in the primaries. He can still achieve a legislative victory without them, one where their party will have no say in the final product.

Republicans are in a difficult bind. If they compromise with President Obama, they might not receive credit if the programs work, and it will be more difficult for the party to disassociate itself from those programs if they fail.

Yet the cost of pure obstructionism -- particularly if the president creates opportunities for bipartisan compromise -- could reproduce an image of the GOP that dogged the party in the 1990s. President Clinton turned the tables on Speaker Newt Gingrich after the Republican takeover of Congress in 1994.

Following the budget battles in 1995 and 1996, Clinton convinced the public that Republicans were not interested in serious governing even when the president reached out his hand, and that Republicans were more interested in scoring points with activists than crafting policy. Congressional Republicans lost their political capital as a majority and were unable to enact much of their agenda.

Though Monday's meeting at the White House will draw most of the attention for the debates that will certainly unfold among Democrats about how far to go with these reductions, what is most important to look for is whether any Republicans step forward and start to offer the outline of viable compromise.

Will they suggest measures the president could take if he wants to realistically expect more than three Republican votes on the bigger issues that he has put on the table?

The opinions expressed in this commentary are solely those of Julian Zelizer.